Deep Q-Learning poor convergence on Stochastic Environment
The inputs that you describe seem like they should be sufficient for a DQN-based agent to learn a good strategy for playing Minesweeper, regardless of whether or not the starting layout changes. The inputs contain all information that is necessary.

However, the problem certainly becomes much easier (probably too easy) if the initial problem is always the same. The DQN algorithm will be very likely to "pick up" on this trend and "exploit" it. The inputs may be sufficient to learn a more general Minesweeper strategy, but if it is consistently faced with the same "level" every single time, it will be much easier for the DQN algorithm to just memorize exactly where the mines are and play perfectly based on that memory, rather than any actual strategy. Due to the way learning is implemented (based on gradient descent), the algorithm will generally tend to converge to such an easily-reachable "memorization" strategy rather than something that is actually "smart".

For that reason, I do think training will be much slower in the case where the layout is randomized. I'm not just thinking along the lines of e.g. twice as slow here, but would expect multiple orders of magnitude more experience required for successful learning. That's just my educated guess though, never tried training DQN for minesweeper specifically so can't tell for sure. It might also require more elaborate hyperparameter tuning, and maybe require a different network architecture (probably require a larger network).